At a restaurant, you can choose from 2 appetizers, 4 main courses, and 3 desserts. How many different meals, each consisting of one appetizer, one main course, and one dessert, can be created?

1 Answer
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources


Write a one sentence answer...



Explain in detail...


I want someone to double check my answer

Describe your changes (optional) 200


This answer has been featured!

Featured answers represent the very best answers the Socratic community can create.

Learn more about featured answers

Apr 17, 2016




First you need to understand the process of selection and arrangement.

Suppose you have 4 numbers - 1, 2, 3, 4 and you have to form 3 digit numbers with all these numbers atmost once (For example 111 is not permitted). How would you do so?

So first step, we have to SELECT 3 numbers from this pile.

We can either choose 1,2,3 or 1,2,4 or 2,3,4 and so on. But how do you definitively know the selections. Here comes in the concept of combinations.

The basic guiding formula for combinations is that
If you have #n# things and you have to select #r# things, the number of selections is represented by #""^nC_r# and

#""^nC_r# = #(n!)/((n-r)! (r!))#

where n! means product of all natural numbers from n to 1. (for eg. if n = 5 then n! = #5xx4xx3xx2xx1# = 120

Here n = 4 and r = 3 so #""^nC_r# = #""^4C_3# = 4 (which are 1,2,3 and 1,2,4 and 2,3,4 and 1,3,4)

Now, you need to ARRANGE these numbers. For this concept, permutations come into play, but I'll leave that for another time as it is not relevant to the question asked by you.

In your question, I just have to SELECT

  1. 1 appetizer from 2 appetizers
  2. 1 main course from 4 main courses
  3. 1 dessert from 3 desserts

Notice how I have capitalized AND. It is because AND is a key word here.
Now what we have to do is get individual selection from the 3 cases and multiply them.

Remember one thing , AND means multiply and OR means add (For eg. if you had said to choose either one main course OR one dessert, then we would have added the selections)

For 1. , selections = #""^2C_1# = 2
For 2. , selections = #""^4C_1# = 4
For 3. , selections = #""^3C_1# = 3

Total possibilites = #""^2C_1 xx ""^4C_1 xx ""^3C_1 = 2xx4xx3 = 24#

Was this helpful? Let the contributor know!
Impact of this question
6005 views around the world
You can reuse this answer
Creative Commons License